| designRandomize {dae} | R Documentation |
Randomize allocated to recipient factors to produce a layout for an experiment
Description
A systematic design is specified by a set of
allocated factors that have been assigned to a set of
recipient factors. In textbook designs the
allocated factors are the treatment factors and the
recipient factors are the factors
indexing the units. To obtain a randomized layout for a systematic design
it is necessary to provide (i) the systematic arrangement of the
allocated factors, (ii) a list of the
recipient factors or a data.frame with
their values, and (iii) the nesting of the
recipient factors for the design being randomized.
Given this information, the allocated factors
will be randomized to the recipient factors,
taking into account the nesting between the recipient factors
for the design.
However, allocated factors that
have different values associated with those recipient
factors that are in the except vector will remain
unchanged from the systematic design.
Also, if allocated is NULL then a random permutation
of the recipient factors is produced
that is consistent with their nesting as specified by
nested.recipients.
For examples of its use also see the vignette accessed via
vignette("DesignNotes", package="dae") and for a discussion of
its use see Brien, Sermarini and Demetro (2023).
Usage
designRandomize(allocated = NULL, recipient, nested.recipients = NULL,
except = NULL, seed = NULL, unit.permutation = FALSE, ...)Arguments
allocated |
A |
recipient |
A If a |
nested.recipients |
A |
except |
A |
seed |
A single |
unit.permutation |
A |
... |
Further arguments passed to or from other methods. Unused at present. |
Details
A systematic design is specified by the
matching of the supplied allocated and recipient
factors. If recipient is a list
then fac.gen is used to generate a data.frame
with the combinations of the levels of the recipient
factors in standard order. Although, the data.frames
are not combined at this stage, the systematic design is
the combination, by columns, of the values of the allocated
factors with the values of recipient
factors in the recipient data.frame.
The method of randomization described by Bailey (1981) is used to
randomize the allocated factors to the
recipient factors. That is, a permutation of the
recipient factors is obtained that respects the
nesting for the design, but does not permute any of the factors in
the except vector. A permutation is generated for all
combinations of the recipient factors, except
that a nested factor, specifed using the
nested.recipients argument, cannot occur in a combination
without its nesting factor(s). These permutations are
combined into a single, units permutation that is
applied to the recipient factors. Then the
data.frame containing the permuted recipient
factors and that containng the unpermuted allocated
factors are combined columnwise, as in cbind. To produce the
randomized layout, the rows of the combined data.frame are
reordered so that its recipient factors are in either
standard order or, if a data.frame was suppled to
recipient, the same order as for the supplied data.frame.
The .Units and .Permutation vectors enable one to
swap between this combined, units permutation and the randomized layout.
The ith value in .Permutation gives the unit to which
unit i was assigned in the randomization.
Value
A data.frame with the values for the recipient and
allocated factors that specify the layout for the
experiment and, if unit.permutation is TRUE, the values
for .Units and .Permutation vectors.
Author(s)
Chris Brien
References
Bailey, R.A. (1981) A unified approach to design of experiments. Journal of the Royal Statistical Society, Series A, 144, 214–223.
See Also
fac.gen, designLatinSqrSys, designPlot, designAnatomy in package dae.
Examples
## Generate a randomized layout for a 4 x 4 Latin square
## (the nested.recipients argument is not needed here as none of the
## factors are nested)
## Firstly, generate a systematic layout
LS.sys <- cbind(fac.gen(list(row = c("I","II","III","IV"),
col = c(0,2,4,6))),
treat = factor(designLatinSqrSys(4), label = LETTERS[1:4]))
## obtain randomized layout
LS.lay <- designRandomize(allocated = LS.sys["treat"],
recipient = LS.sys[c("row","col")],
seed = 7197132, unit.permutation = TRUE)
LS.lay[LS.lay$.Permutation,]
## Generate a randomized layout for a replicated randomized complete
## block design, with the block factors arranged in standard order for
## rep then plot and then block
## Firstly, generate a systematic order such that levels of the
## treatment factor coincide with plot
RCBD.sys <- cbind(fac.gen(list(rep = 2, plot=1:3, block = c("I","II"))),
tr = factor(rep(1:3, each=2, times=2)))
## obtain randomized layout
RCBD.lay <- designRandomize(allocated = RCBD.sys["tr"],
recipient = RCBD.sys[c("rep", "block", "plot")],
nested.recipients = list(plot = c("block","rep"),
block="rep"),
seed = 9719532,
unit.permutation = TRUE)
#sort into the original standard order
RCBD.perm <- RCBD.lay[RCBD.lay$.Permutation,]
#resort into randomized order
RCBD.lay <- RCBD.perm[order(RCBD.perm$.Units),]
## Generate a layout for a split-unit experiment in which:
## - the main-unit factor is A with 4 levels arranged in
## a randomized complete block design with 2 blocks;
## - the split-unit factor is B with 3 levels.
## Firstly, generate a systematic layout
SPL.sys <- cbind(fac.gen(list(block = 2, main.unit = 4, split.unit = 3)),
fac.gen(list(A = 4, B = 3), times = 2))
## obtain randomized layout
SPL.lay <- designRandomize(allocated = SPL.sys[c("A","B")],
recipient = SPL.sys[c("block", "main.unit", "split.unit")],
nested.recipients = list(main.unit = "block",
split.unit = c("block", "main.unit")),
seed=155251978)
## Generate a permutation of Seedlings within Species
seed.permute <- designRandomize(recipient = list(Species = 3, Seedlings = 4),
nested.recipients = list(Seedlings = "Species"),
seed = 75724, except = "Species",
unit.permutation = TRUE)